What is |x^2-2x|+|x-4|>|x^2-3x+4| ?

The solution to |x^2-2x|+|x-4|>|x^2-3x+4| is 0 4

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|x^2-2x|+|x-4|>|x^2-3x+4|

x^{2} - 2 x + ∣ x - 4 ∣ > x^{2} - 3 x + 4

0 < x < 2 or x > 4

Solution steps

x^{2} - 2 x + ∣ x - 4 ∣ > x^{2} - 3 x + 4

Find positive and negative intervals

x \leq 0, 0 < x < 2, 2 \leq x < 4, x \geq 4

Solve the inequality for each interval

No Solution or 0 < x < 2 or x > 4

Merge Overlapping Intervals

0 < x < 2 or x > 4

x^{2} - 4 x < 5

x^{2} - 5 x < 6

x^{2} - 2 x < x

x^{2} + x > x^{2} + 5 x - 8

∣ x + 3 ∣ > ∣ 2 x - 1 ∣

What is |x^2-2x|+|x-4|>|x^2-3x+4| ?
The solution to |x^2-2x|+|x-4|>|x^2-3x+4| is 0<x<2\lor x>4